write in words
3a- 6
[tex] \frac{1}{2} z \: fy \: 10[/tex]
​

Answer:

Area of given triangle is 939.15cm² and smallest altitude is 30.8cm

We are given three sides of a triangle, Let the sides be :

We can find the area of the triangle with its three sides using Heron's Formula

Heron's formula was founded by hero of Alexandria, for finding the area of triangle in terms of the length of its sides. Heron's formula can be written as:

[tex] \sf{ \pmb { \longrightarrow \: \sqrt{s(s - a)(s - b)(s - c)} }}[/tex]

where ( s ) :

[tex] \sf \longrightarrow s = \dfrac{a + b + c}{2} [/tex]

Therefore, for the given triangle first we will calculate ( s )

[tex] \begin {aligned}\quad & \quad \longmapsto \sf s = \dfrac{a + b + c}{2} \\ & \quad \longmapsto \sf s = \dfrac{35 + 54 + 61}{2} \\ & \quad \longmapsto \sf s = \dfrac{150}{2} \\ & \quad \longmapsto \sf s = 75cm \end{aligned}[/tex]

Now, Area of triangle will be:

[tex] \begin{aligned}&:\implies \sf\quad \sf \: A = \sqrt{s(s - a)(s - b)(s - c)} \\ &:\implies \sf\quad \sf \: A = \sqrt{75(75 - 35)(75 - 54)(75 - 61)} \\&:\implies \sf\quad \sf \: A = \sqrt{75 \times 40 \times 21 \times 14} \\ &:\implies \sf\quad \sf \: A = \sqrt{5 \times 5 \times 3 \times 3 \times 2 \times 2 \times 7 \times 7 \times 2 \times 2 \times 5} \\ &:\implies \sf\quad \sf \: A =5 \times 3 \times 2 \times 7 \times 2 \sqrt{5} \\ &:\implies \sf\quad \sf \: A =420 \times 2.23 \\ &:\implies \sf\quad \sf \boxed{ \pmb{ \sf A =939.15 {cm}^{2} }} \end{aligned}[/tex]

Also, we have to find the smallest altitude, and the smallest altitude will be on the longest side. So,

[tex] \begin{aligned}&:\implies \sf\quad \sf \: Area =939.15 \\ &:\implies \sf\quad \sf \: \dfrac{1}{2} \times b \times h =939.15 \\ &:\implies \sf\quad \sf \: \dfrac{1}{2} \times 61 \times h = 939.15 \\&:\implies \sf\quad \sf \: h =939.15 \times \dfrac{2}{61} \\&:\implies \sf\quad \sf \: h = \dfrac{1818.3}{61} \\ &:\implies \sf\quad \boxed{ \pmb{\sf \: h =30.79 \: (approx)}} \end{aligned}[/tex]

Answer:

Area = 939.15 cm² (2 d.p.)

Shortest Altitude = 30.79 cm (2 d.p.)

Step-by-step explanation:

Heron's Formula allows us to find the area of a triangle in terms its side lengths.

Heron's Formula

[tex]\sf Area = \sqrt{s(s-a)(s-b)(s-c)}[/tex]

where:

Given values:

Find the value of s:

[tex]\sf \implies s=\dfrac{a+b+c}{2}=\dfrac{35+54+61}{2}=75\:cm[/tex]

Substitute the values into the formula and solve for area:

[tex]\begin{aligned}\implies \sf Area & =\sf \sqrt{75(75-35)(75-54)(75-61)}\\& = \sf \sqrt{75(40)(21)(14)}\\& = \sf \sqrt{882000}\\& = \sf \sqrt{176400 \cdot 5}\\& = \sf \sqrt{176400}\sqrt{5}\\& = \sf 420\sqrt{5}\\& = \sf 939.15\:\:cm^2\:\:(2\:d.p.)\end{aligned}[/tex]

The altitude of a triangle is a perpendicular line segment drawn from a vertex of the triangle to the side opposite to it.

The shortest altitude of a triangle is drawn to the longest side.

Therefore, the shortest altitude will be the height of the triangle when the longest side is the base:

[tex]\begin{aligned}\textsf{Area of a Triangle} & = \sf \dfrac{1}{2} \times base \times height\\\implies \sf 420\sqrt{5} & = \sf \dfrac{1}{2} \times 61 \times altitude \\\implies \sf Altitude & = \sf \frac{2 \cdot 420\sqrt{5}}{61}\\& = \sf \dfrac{840\sqrt{5}}{61}\\ & = \sf 30.79\:\:cm\:\:(2\:d.p.)\end{aligned}[/tex]

Answer:

12 :)

Step-by-step explanation:

18/3 = 6

Now we multiply :)

6 x 2 = 12

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

12

Step-by-step explanation:

2/3 of 18 =

1/3 of 18 = 6

(because 18 divided by 3 = 6)

2/3 of 18 = 1/3 + 1/3

therefore 2/3 of 18 = 6 + 6 = 12 (or 6 x 2)

Hope this makes sense! If you have further questions, let me know!

- profparis

a brainliest would be appreciated if i helped you! :D

Z-scores are used to determine the probability of data. The z-score for the given parameters in normal distribution is -6.35

The formula given to calculate the z-score is expressed as:

[tex]z = \dfrac{x-\mu}{\frac{\sigma}{\sqrt{n}} }[/tex]

Given the following parameters:

Mu = 1.36

n = 28
[tex]\sigma = 5[/tex]

Mean = 130

Substitute into the formula

[tex]z = \dfrac{130-136}{\frac{5}{\sqrt{28}} }\\ x = \frac{-6}{0.9449} \\z = -6.35[/tex]

Hence the z-score for the given parameters in normal distribution is -6.35

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Answer:

step 1 is the answer

if you like my answer please like comment and mark me as brilliant

Answer:

D - The subtraction property of equality was not applied to solve this equation

Step-by-step explanation:

I got it right on the test

Explanation - they added 7 to both sides, so there was no subtraction property used

Answer:

53

Step-by-step explanation:

[tex]sum \: of \: angles = 180 \\ 180 = 74 + 2x \: where \: x \: is \: the \: measure \: of \: the \: other \: angles \\ 180 - 74 = 2x \\ 106 = 2x \\ x = \frac{106}{2} \\ x = 53[/tex]

Always welcome

Answer:

•WHAT IS PERIMETER?

>> PERIMETER MEANS THE SUM OF ALL SIDES OF FIGURE

NOW,LET'S SEE YOUR GIVEN QUESTION.

THE FIGURES 2 SIDES DATA IS GIVEN

•6CM

•5.5CM

THEREFORE : 6 + 5.5

: 11.5 CM

THE PERIMETER OF FIGURE IS 11.5 CM

Answer:

500 grams

Step-by-step explanation:

we can conclude that the mass of each box is 0.5 kg by dividing 4 by 8

0.5 kg is 500 grams

Answer:

12 cups

Step-by-step explanation:

The ratio he uses is

2 parts strong coffee

3 parts milk

Let's say he makes a recipe exactly like the amounts of the ratio.

2 cups strong coffee

3 cups milk

Total: 2 cups + 3 cups = 5 cups

He wants to make 30 cups, so 5 cups is not enough.

Let's double the amounts of the recipe keeping the same ratio of 2 to 3.

2 × 2 = 4 cups strong coffee

3 × 2 = 6 cups milk

Total: 4 cups + 6 cups = 10 cups

He wants to make 30 cups, so 10 cups is not enough.

We can keep on going up by multiplying the numbers in the ratio by larger numbers, but there is a quicker way.

We need to multiply both numbers in the ratio by a number, let's call it x, so that when both numbers in the ratio are multiplled by x, and the ingredients are added, we end up with 30 cups.

Multiply both numbers in the ratio by x.

2x cups of strong coffee

3x cups of milk

Now add: the total amount will be 5x cups

We want 30 cups, so

5x = 30

Solve for x.

x = 30/5 = 6

x, the multiplier we need is 6.

2x cups strong coffee = 2(6) cups = 12 cups

3x cups milk = 3(6) cups = 18 cups

Answer: 12 cups

Answer:

49.67ft

Step-by-step explanation:

i used the internet, use it too

We have been provided with the total surface area of cube that is 150cm².

So here we will first find out the value of a side of cube.

★ Total surface area of cube :-

Here,

Putting the values,

6a² = 150cm²

a² = 150 / 6

a² = 50 / 2

a² = 25

a = √25

a = 5

Henceforth,

★ Finding out volume of cube :-

As we know that volume of cube is calculated by the formula :

Putting the values,

V = 5³

V = 5 × 5 × 5

V = 25 × 5

V = 125

Henceforth,

Answer: I took the test and this is the answer.

Answer:

I think there's 502

Step-by-step explanation:

if this is a olunomical question that should be it I believe, because you have to write in standered form then when it equals zero, then factor it

Answer:

f(0)=6

Step-by-step explanation:

It should be the third one because it is the only one that has the x-value in the parentheses and equals the y-value. (I think please someone back me up)

Answer:

-14 > -23

Step-by-step explanation:

-14 is greater than -23 since it is closer to 0 than -23.

hope this helps!! p.s. i really need brainliest :)

Answer:

a.

Step-by-step explanation:

open chormecanvis and draw little cubes on the side of the prisum, thats wahat i did

Step-by-step explanation:

[tex]put \: x \: into \: equation \: 1[/tex]

[tex]2( - 6y + 7) - 9y = 14[/tex]

[tex] - 12y + 14 - 9y = 14[/tex]

[tex] - 21y + 14 = 14[/tex]

[tex] - 21y = 14 - 14[/tex]

[tex] - 21y = 0[/tex]

[tex] \frac{ - 21y}{12} = \frac{0}{21} [/tex]

[tex]y = 0[/tex]

[tex]put \: y = 0 \: into \: equation \: 2[/tex]

[tex]x = 6y + 7[/tex]

[tex]x = 6(0) + 7[/tex]

[tex]x = 0 + 7[/tex]

[tex]x = 7[/tex]

Answer:

y = 0

x = 7

Step-by-step explanation:

2x − 9y = 14     ⇒  ( 1 )

x = − 6y +7      ⇒ ( 2 )

First, let us find the value of y.

For that, replace x with ( - 6y + 7 ).

Let us take equation 1 for that.

2x − 9y = 14

2 ( - 6y + 7 ) - 9y = 14

-12y + 14 - 9y = 14

21y = 14 - 14

21y = 0

Divide both sides by 21.

y = 0

And now let us take equation 2 to find the value of x by replacing y with 0.

2x − 9y = 14    

2x - 9 × 0 = 14

2x - 0 = 14

2x = 14

Divide both sides by 2.

x = 7

Answer:

About 1885 sq. ft

Step-by-step explanation:

[tex]v = \pi \: (10)^{2} (6) [/tex]

Since the radius is 10ft and the height of the cylinder is 6 ft you substitute that into the formula and you receive 1884.96.

If Reducing 2 men will bbe enough too finish the work in 10 days

For rate of work use the formualar

rate of work = quantity of work / duration

10 men can do the work at a rate of  =  1 / 8

x men can do same work at a rate of = 1 / 10

x * ( 1 / 8 ) = 10 * ( 1 / 10 )

x = 1 * 8 = 8

therefore 8 men can do the work in 10 days

number of men reduced = 10 men - 8 men = 2 men

Hope it helped

Answer:

4z+3

Step-by-step explanation:

multiply the z's giving four z's and we don't know the value of z so we can't add 3 to it

Answer:

x = 5

Step-by-step explanation:

Any number over 0 is undefined. Given that, the values of x that make this expression undefined make the denominator equal to 0

x - 5 = 0

x = 5

I hope this helps!

Answer:

48 ≥ 4x + 2y

44 ≥ 2x + 2y

    First, we will look at assembling hours.

"The standard model requires 4 hours to assemble [and] the artisan model requires 2 hours to assemble"

    We also know they have 48 hours per day for assembly, x is standard model and y is artisan model.

48 = 4x + 2y

    Lastly, they do not need to make that many, but they can so we will use greater than or equal to.

48 ≥ 4x + 2y

    Now let us look at finishing hours.

"The standard model requires ... 2 hours for finishing touches. The artisan model requires ... 2 hours for finishing touches."

    We also know they have 44 hours per day for assembly, x is standard model and y is artisan model.

44 = 2x + 2y

    Again, they do not need to make that many, but they can so we will use greater than or equal to.

44 ≥ 2x + 2y

Answer:

[tex] -\frac{1}{2}x^2-2x-5 [\tex]

Step-by-step explanation:

To convert it to standard form, all you need to do is expand the square and simplify. This would get us to: [tex]-\frac{1}{2}(x^2 + 4x + 4) - 3[/tex] which simplifies further to [tex]-\frac{1}{2}x^2-2x-2-3[/tex] and combine the -2 and -3 to get [tex] -\frac{1}{2}x^2-2x-5 [\tex]

Hope this helps :)

Answer:

y = -3/2x + 3

Step-by-step explanation:

slope-intercept form: y - y₁ = m (x - x₁)

y - 9 = -3/2 ( x + 4)

y = -3/2 x - 6 + 9

y = -3/2x + 3

PLEASE RATE!! I hope this helps!!

If you have any questions comment below

Answer:

[tex] \frac{0.75x - 3}{x - 1} [/tex]

Step-by-step explanation:

Equation of a rational function is

[tex] \frac{p(x}{q(x)} [/tex]

where q(x) isn't zero.

There is a vertical asymptote at

[tex]x = 1[/tex]

So this mean that our denomiator must have a zero that occur at x=1.

That zero is

[tex]x - 1[/tex]

So our denomiator is

[tex] \frac{p(x)}{x - 1} [/tex]

Since our horinzontal asymptote is a non zero value, the numerator must be a linear equation as well.

So our rational function is

[tex] \frac{ax + b}{x - 1} [/tex]

We know the graph pass through (0,3)

So if we apply that logic,

[tex] \frac{a(0) + b}{0 - 1} = 3[/tex]

[tex] \frac{b}{ - 1} = 3[/tex]

[tex]b = - 3[/tex]

And it passes through (4,0)

[tex] \frac{a(4) + b}{3} = 0[/tex]

[tex]4a + b = 0[/tex]

[tex]4a + ( - 3) = 0[/tex]

[tex]4a = 3[/tex]

[tex]a = \frac{3}{4} [/tex]

So our rational equation is

[tex] \frac{0.75x - 3}{x - 1} [/tex]

It will take 27 containers of 1/3 liter to fill the tank.

Since you need 3 containers of 1/3 to have a full liter, and 9 liters for the tank, 9*3=27.

Answer:

27

Step-by-step explanation:

1= 1/3x3

3x9=27

Answer:

Step-by-step explanation:

This is a proportion question which is 2 ratios which are equal to one another. If 3 of the 4 parts are known, the 4th part can be calculated.

36 liters.

36 km/3 Liters = x / 36             multiply both sides by 36

36*36 / 3 =  x

1296/3 = x

x = 432 km

So on 36 L he can go 432 km

3 liters

Given as 36 km

48 liters

36km/3 liters = x / 48 liters         Multiply both sides by 48

48*36/3 = x

576 km = x

So on 48 liters, he can go 576 km

132 liters

36 km/ 3 liters = x/132

x = 1564 km

On 132 liters Pat can go 1564 km

Answer:

25,515

Step-by-step explanation:

35 x 27 x 27

945 x 27

25,515

Answer:

We can think of our denominator as 6 in our probability, because there are 6 total sides to this die.

Out of those 6 sides, they want to find out if we can roll a number less than 3.

First, let's find how many numbers there are on this die that are less than 3.

1 and 2, so there are 2 sides that contain numbers less than 3 on this die.

So there is a 2 out of 6 chance(2/6) which can be simplified to 1/3, of selecting a number less than 3 when rolling a die.

1/3 probability.

Convert this into a percent if you'd want:-

1/3 · 100

= 33.333... which can be rounded to a 33% probability.

Assuming this economy is closed: Consumption $6.9 trillion; Government Purchases $11.2 trillion; National Saving $2.3 trillion; Investment $2.3 trillion.

a. Consumption

Private S = ( Y – T – C )

C = Y - T - Private S

C = $12 - $3.6 - $1.5 =$6.9 trillion

b. Government purchases

Public S = ( T - G )          

G = T - Public S                                                        

G = $12 - $0.8

G = $11.2 trillion

c and d. National saving and investment

National savings = Public S + Private S

National savings = $0.8 + $1.5

National savings =$2.3 trillion

Investment=Savings=$2.3 trillion

Therefore, Consumption $6.9 trillion; Government Purchases $11.2 trillion; National Saving $2.3 trillion; Investment $2.3 trillion.

Learn more about GDP here:https://brainly.com/question/1383956